Wavelet coefficients measuring smoothness in H p(ℝd)

Abstract

We investigate the connection between Besov spaces and certain approximation subspaces of the Hardy spaces Hp(ℝd), 0 < p ≤ 1. In particular, we establish the wavelet decompositions for the Hp(ℝd) spaces and we characterize the homogeneous Besov spaces Ḃs p,q(ℝd) in terms of the wavelet coefficients of such decompositions, under minimal decay and smoothness conditions on the wavelet set Ψ. In the process, we also obtain a new characterization of the Ḃs p,q(ℝd) spaces in terms of the modulus of smoothness measured in the norm of Hp(ℝd). © 1996 Academic Press, inc.